Answer:
112cm²/sec
Step-by-step explanation:
Area of a square is expressed as A = L² where L is the length of one side of the square.
The rate of change of area will be expressed using chain rule as;
dA/dt = dA/dL * dL/dt where;
dL/dt is the rate at which the side length of the square is decreasing.
Given L = 7cm, dL/dt = 8cm/sec and dA/dL = 2L
dA/dL = 2(7)
dA/dL = 14cm
Substituting the given value into the chain rule expression above to get the rate of change of the area of the square, we will have;
dA/dt = dA/dL * dL/dt
dA/dt = 14cm * 8cm/sec
dA/dt = 112cm²/sec
Hence, the rate of change of the area of the square when the side length is 7 cm is 112cm²/sec
